Finite Group Databasebeta

← #28247673

Subgroups — #28247673

Order 13568.

4902 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811459C211yesmaximal, characteristic
2C2×#16811389C211yesmaximal, characteristic, complemented
3C2×#16811103C211yesmaximal, characteristic, complemented
4#20283247C214yesmaximal, complemented
5#20283244C214yesmaximal, complemented
6#20283240C214yesmaximal, complemented
7#20283237C214yesmaximal, complemented
8#20283232C211yesmaximal, characteristic, complemented
9#20283231C214yesmaximal, complemented
10C2×#16810625C211yesmaximal, characteristic, complemented
11C2×#16810624C211yesmaximal, characteristic, complemented
12#417×D53C214yesmaximal, complemented
13C53×#2896C211yesmaximal, characteristic, complemented
14#16811459—28no—
15#16811459C4116yescomplemented
16C2×#13133265C2212yes—
17C2×#13133264—21no—
18C2×#13133264C2212yes—
19C2×#13133263—21no—
20C2×#13133263C2212yes—
21C2×#13133262—22no—
22C2×#13133262C2212yes—
23C22×#11719945—22no—
24C22×#11719945C2211yescharacteristic
25C22×#11719945C2211yescharacteristic
26C2×#41×D53—22no—
27C2×#41×D53C2214yes—
28#16811389—28no—
29C2×#13133225C2214yescomplemented
30C2×#13133223C2214yescomplemented
31C22×#11719917C2211yescharacteristic, complemented
32C2×M16×D53C2214yescomplemented
33#16811103—22no—
34#16811103—22no—
35#16811103C2214yescomplemented
36#16811103C2214yescomplemented
37C2×C4×Dic106—21no—
38C2×C4×D212—21no—
39C2×#13133177—22no—
40C2×#13133175C2212yescomplemented
41C22×C4⋊Dic53C2211yescharacteristic, complemented
42C2×C4⋊C4×D53C2212yescomplemented
43#16810631C2212yescomplemented
44#16810630C2218yescomplemented
45#16810627C2212yescomplemented
46#16810626C2218yescomplemented
47#16810625C2214yescomplemented
48#16810625C2214yescomplemented
49#16810624C2214yescomplemented
50#16810624C2214yescomplemented
51#16810623C2218yescomplemented
52#16810622C2212yescomplemented
53#16810622C2212yescomplemented
54#16810621C2218yescomplemented
55#16810618C2218yescomplemented
56#16810617C2214yescomplemented
57#16810616C2218yescomplemented
58C2×#13133142C2212yescomplemented
59C2×#13133141C2212yescomplemented
60#103×D53C2218yescomplemented
61C2×#13133139C2212yescomplemented
62C2×#13133138C2212yescomplemented
63#102×D53C2218yescomplemented
64C22×#41×C53C2211yescharacteristic
65C22×M16×C53C2211yescharacteristic, complemented
66C2×#117×C53C2211yescharacteristic, complemented
67C53×#419C2212yescomplemented
68C53×#418C2212yescomplemented
69C53×#417C2212yescomplemented
70C53×#417C2212yescomplemented
71C53×#416C2214yescomplemented
72#13133265—28no—
73#13133265C2×C4116yescomplemented
74#13133264—28no—
75#13133264—216no—
76#13133264C2×C4116yescomplemented
77#13133263—28no—
78#13133263—216no—
79#13133263C2×C4116yescomplemented
80#13133262—232no—
81#13133262—28no—
82#13133262C2×C4116yescomplemented
83C2×#11719949—22no—
84C2×#11719949C2314yes—
85C2×#11719945—21no—
86C2×#11719945—21no—
87C2×#11719945—24no—
88C2×#11719945—24no—
89C2×#11719945—232no—
90C2×#11719945—22no—
91C2×#11719945—24no—
92C2×#11719945—22no—
93C2×#11719945C2×C418yes—
94C2×#11719945C2×C418yescomplemented
95C2×#11719945D418yes—
96C2×#11719945D412yes—
97C2×#11719945D412yes—
98C2×#11719945C2312yes—
99C2×#11719945C2312yes—
100C2×#11719945C2312yes—
101C2×#11719945C2312yes—
102C2×#11719947—24no—
103C2×#11719947—24no—
104C2×#11719947—22no—
105C2×#11719947C2314yes—
106#41×D53—232no—
107#41×D53—216no—
108#41×D53C2×C4132yescomplemented
109C22×Dic106—22no—
110C22×Dic106D411yescharacteristic
111C22×Dic106C2311yescharacteristic
112C2×Q8×D53—22no—
113C2×Q8×D53C2314yes—
114C22×D212—22no—
115C22×D212D411yescharacteristic
116C22×D212C2311yescharacteristic
117C22×C22⋊D53—21no—
118C22×C22⋊D53—24no—
119C22×C22⋊D53D412yes—
120C2×D4×D53—24no—
121C2×D4×D53—24no—
122C2×D4×D53—22no—
123C2×D4×D53C2314yes—
124C23×Dic53—21no—
125C22×C4×D53—21no—
126C22×C4×D53—24no—
127C22×C4×D53—22no—
128C22×C4×D53C2312yes—
129#13133225—216no—
130#13133223—216no—
131C2×#11719917—24no—
132C2×#11719917C2312yes—
133C2×#11719917C2312yes—
134C2×#11719912C2318yes—
135M16×D53—216no—
136C22×#88322C2312yes—
137C2×C8×D53C2318yes—
138C4×Dic106—24no—
139C4×Dic106—24no—
140C4×D212—24no—
141C4×D212—24no—
142#13133177—28no—
143#13133177—28no—
144#13133175—24no—
145#13133175C2318yes—
146C2×C4⋊Dic53—21no—
147C2×C4⋊Dic53—21no—
148C2×C4⋊Dic53—21no—
149C2×C4⋊Dic53C2312yes—
150C2×C4⋊Dic53C2312yes—
151C2×C4⋊Dic53C2312yes—
152C2×#11719919—22no—
153C4⋊C4×D53—24no—
154C4⋊C4×D53C2318yes—
155C2×#11719921—22no—
156C2×C4×Dic53—22no—
157#13133142C2318yes—
158#13133141C2318yes—
159#13133140C2314yes—
160#13133140C2314yes—
161#13133139C2318yes—
162#13133138C2318yes—
163#13133137C2314yes—
164#13133137C2314yes—
165C2×#41×C53—21no—
166C2×#41×C53—21no—
167C2×#41×C53—24no—
168C2×#41×C53C2×C418yescomplemented
169C2×#41×C53C2312yes—
170C2×#41×C53C2312yes—
171C22×Q8×C53C2311yescharacteristic
172C22×D4×C53—21no—
173C22×D4×C53C2311yescharacteristic
174C23×C4×C53—21no—
175C23×C4×C53C2311yescharacteristic
176C2×M16×C53—24no—
177C2×M16×C53C2312yes—
178C2×M16×C53C2312yes—
179C22×C8×C53C2312yes—
180#117×C53—21no—
181#117×C53—21no—
182#117×C53C2312yes—
183#117×C53C2312yes—
184C2×C4⋊C4×C53C2311yescharacteristic
185C2×C4⋊C4×C53C2311yescharacteristic
186C2×C22⋊C4×C53—21no—
187C2×C42×C53—21no—
188#103×C53C2314yes—
189#103×C53C2314yes—
190#102×C53C2314yes—
191#102×C53C2314yes—
192C24×C53—21no—
193C24×C53C2×D411yescharacteristic
194C23×D53—21no—
195C23×D53—24no—
196C23×D53C2×D412yes—
197#41×C53—28no—
198#41×C53—28no—
199#41×C53—24no—
200#41×C53—24no—
201#41×C53C22×C418yes—
202#41×C53C22×C418yescomplemented
203C2×Q8×C53—21no—
204C2×Q8×C53—22no—
205C2×Q8×C53C22×C414yescomplemented
206C2×Q8×C53C2412yes—
207C2×D4×C53—28no—
208C2×D4×C53—22no—
209C2×D4×C53—22no—
210C2×D4×C53—21no—
211C2×D4×C53—22no—
212C2×D4×C53C22×C414yescomplemented
213C2×D4×C53C2412yes—
214C22×C4×C53—21no—
215C22×C4×C53—28no—
216C22×C4×C53—22no—
217C22×C4×C53—22no—
218C22×C4×C53—21no—
219C22×C4×C53—21no—
220C22×C4×C53C22×C414yes—
221C22×C4×C53C2×D411yescharacteristic
222C22×C4×C53C2×D411yescharacteristic
223C22×C4×C53C2×D411yescharacteristic
224C22×C4×C53C2×D414yes—
225C22×C4×C53C2411yescharacteristic
226C22×C4×C53C2411yescharacteristic
227C22×C4×C53C2411yescharacteristic
228C2×C22⋊D53—28no—
229C2×C22⋊D53—22no—
230C2×C22⋊D53—22no—
231C2×C22⋊D53—24no—
232C2×C22⋊D53—232no—
233C2×C22⋊D53—24no—
234C2×C22⋊D53C22⋊C4116yes—
235C2×C22⋊D53C2×D414yes—
236C2×C22⋊D53C2×D414yes—
237C22×Dic53—21no—
238C22×Dic53—24no—
239C22×Dic53—22no—
240C22×Dic53—22no—
241C22×Dic53—22no—
242C22×Dic53—82no—
243C22×Dic53C2×D412yes—
244#11719949—216no—
245#11719949—28no—
246#11719949C22×C4116yescomplemented
247Q8×D53—28no—
248Q8×D53—216no—
249Q8×D53C22×C4116yescomplemented
250#11719947—232no—
251#11719947—232no—
252#11719947—28no—
253#11719947—216no—
254#11719947C22×C4116yescomplemented
255D4×D53—232no—
256D4×D53—232no—
257D4×D53—216no—
258D4×D53—28no—
259D4×D53C22×C4116yescomplemented
260#11719945—28no—
261#11719945—28no—
262#11719945—24no—
263#11719945—24no—
264#11719945—232no—
265#11719945—216no—
266#11719945—232no—
267#11719945—216no—
268#11719945C22⋊C4116yes—
269#11719945C22⋊C4116yes—
270#11719945C22×C418yes—
271#11719945C22×C418yes—
272#11719945C22×C418yes—
273#11719945C22×C418yescomplemented
274#11719945C2×D418yes—
275#11719945C2×D418yes—
276C2×D212—24no—
277C2×D212—21no—
278C2×D212—22no—
279C2×D212—216no—
280C2×D212C22⋊C418yes—
281C2×D212C22×C414yescomplemented
282C2×D212C2×D412yes—
283C2×D212C2×D412yes—
284C2×D212C2412yes—
285C2×C4×D53—24no—
286C2×C4×D53—28no—
287C2×C4×D53—22no—
288C2×C4×D53—22no—
289C2×C4×D53—24no—
290C2×C4×D53—232no—
291C2×C4×D53—28no—
292C2×C4×D53—84no—
293C2×C4×D53C22×C418yes—
294C2×C4×D53C2×D414yes—
295C2×C4×D53C2×D418yes—
296C2×C4×D53C2414yes—
297C2×Dic106—21no—
298C2×Dic106—22no—
299C2×Dic106—24no—
300C2×Dic106—216no—
301C2×Dic106C22⋊C418yes—
302C2×Dic106C22×C414yescomplemented
303C2×Dic106C2×D412yes—
304C2×Dic106C2×D412yes—
305C2×Dic106C2412yes—
306M16×C53—24no—
307M16×C53—24no—
308C2×C8×C53—24no—
309C2×C8×C53C2414yes—
310C4⋊C4×C53—21no—
311C4⋊C4×C53—21no—
312C4⋊C4×C53C2412yes—
313C4⋊C4×C53C2412yes—
314C22⋊C4×C53—22no—
315C22⋊C4×C53—22no—
316C42×C53—22no—
317C42×C53—22no—
318#11719921—28no—
319C4⋊Dic53—22no—
320C4⋊Dic53—22no—
321C4⋊Dic53—22no—
322C4⋊Dic53C2414yes—
323#11719919—28no—
324C4×Dic53—28no—
325#11719917—24no—
326#11719917—24no—
327C2×#88322—24no—
328C2×#88322C2414yes—
329#11719912—216no—
330C8×D53—216no—
331C23×C53—22no—
332C23×C53—24no—
333C23×C53—41no—
334C23×C53—41no—
335C23×C53—81no—
336C23×C53—81no—
337C23×C53C2×C22⋊C414yes—
338C23×C53C22×D411yescharacteristic
339C23×C53C22×D411yescharacteristic
340C23×C53C22×D411yescharacteristic
341C22×D53—22no—
342C22×D53—24no—
343C22×D53—216no—
344C22×D53—42no—
345C22×D53—42no—
346C22×D53—84no—
347C22×D53—84no—
348C22×D53—81no—
349C22×D53—81no—
350C22×D53C2×C22⋊C418yes—
351C22×D53C22×D414yes—
352Q8×C53—24no—
353Q8×C53—22no—
354Q8×C53C23×C414yes—
355D4×C53—28no—
356D4×C53—28no—
357D4×C53—24no—
358D4×C53—22no—
359D4×C53C23×C414yes—
360C2×C4×C53—24no—
361C2×C4×C53—22no—
362C2×C4×C53—28no—
363C2×C4×C53—28no—
364C2×C4×C53—22no—
365C2×C4×C53—22no—
366C2×C4×C53—42no—
367C2×C4×C53—42no—
368C2×C4×C53C2×C22⋊C414yes—
369C2×C4×C53C2×C22⋊C414yes—
370C2×C4×C53C2×C22⋊C414yes—
371C2×C4×C53C23×C412yes—
372C2×C4×C53C23×C412yes—
373C2×C4×C53C23×C412yes—
374C2×C4×C53C22×D411yescharacteristic
375C2×C4×C53C22×D411yescharacteristic
376C2×C4×C53C22×D411yescharacteristic
377C2×C4×C53C22×D412yes—
378C2×C4×C53C22×D412yes—
379C2×C4×C53C22×D412yes—
380C2×C4×C53C2511yescharacteristic
381C22⋊D53—28no—
382C22⋊D53—28no—
383C22⋊D53—216no—
384C22⋊D53—216no—
385C22⋊D53C2×C22⋊C4116yes—
386C22⋊D53C2×C22⋊C4116yes—
387C2×Dic53—24no—
388C2×Dic53—22no—
389C2×Dic53—216no—
390C2×Dic53—24no—
391C2×Dic53—44no—
392C2×Dic53—82no—
393C2×Dic53—82no—
394C2×Dic53C2×C22⋊C418yes—
395C2×Dic53C22×D414yes—
396D212—216no—
397D212—24no—
398D212—22no—
399D212C2×C22⋊C418yes—
400D212C2×C22⋊C418yes—
401D212C23×C414yes—
402C4×D53—216no—
403C4×D53—28no—
404C4×D53—28no—
405C4×D53—216no—
406C4×D53—88no—
407C4×D53C2×C22⋊C4116yes—
408C4×D53C23×C418yes—
409C4×D53C22×D418yes—
410Dic106—24no—
411Dic106—22no—
412Dic106—216no—
413Dic106C2×C22⋊C418yes—
414Dic106C2×C22⋊C418yes—
415Dic106C23×C414yes—
416C8×C53—24no—
417#88322—24no—
418#60089—531nomaximal, Sylow
419C22×C53—21no—
420C22×C53—21no—
421C22×C53—21no—
422C22×C53—21no—
423C22×C53—21no—
424C22×C53—21no—
425C22×C53—24no—
426C22×C53—44no—
427C22×C53—42no—
428C22×C53—42no—
429C22×C53—84no—
430C22×C53C22×C22⋊C412yes—
431C22×C53C22×C22⋊C412yes—
432C22×C53C22×C22⋊C412yes—
433C22×C53C23×D411yescharacteristic
434C2×D53—24no—
435C2×D53—24no—
436C2×D53—24no—
437C2×D53—48no—
438C2×D53—42no—
439C2×D53—42no—
440C2×D53—816no—
441C2×D53—84no—
442C2×D53C22×C22⋊C418yes—
443C4×C53—24no—
444C4×C53—42no—
445C4×C53—42no—
446C4×C53C22×C22⋊C412yes—
447C4×C53C22×C22⋊C412yes—
448C4×C53C22×C22⋊C412yes—
449C4×C53C24×C411yescharacteristic
450C4×C53C23×D411yescharacteristic
451Dic53—24no—
452Dic53—44no—
453Dic53C22×C22⋊C418yes—
454C2×#585—531no—
455C2×#568—531no—
456C2×#520—531no—
457#2898—534no—
458#2898—534no—
459#2897—534no—
460#2897—534no—
461#2896—534no—
462#2896—531no—
463#2896D5311yescharacteristic, complemented
464C2×#417—534no—
465C2×#417—531no—
466C2×#417—531no—
467C2×C53—22no—
468C2×C53—22no—
469C2×C53—22no—
470C2×C53—44no—
471C2×C53C23×C22⋊C411yescharacteristic
472C2×C53#358511yescharacteristic
473C2×C53#358611yescharacteristic
474D53—28no—
475D53—44no—
476#585—5316no—
477#585—1068no—
478C2×2−1+4—532no—
479C2×2−1+4—532no—
480C2×2−1+4—1061no—
481C2×H(5,𝔽2)—532no—
482C2×H(5,𝔽2)—532no—
483C2×H(5,𝔽2)—1062no—
484C2×H(5,𝔽2)—1061no—
485C22×#41—531no—
486C22×#41—534no—
487C22×#41—531no—
488C22×#41—1062no—
489C22×#41—1062no—
490C22×#41C2×D5311yescharacteristic
491#568—1068no—
492C2×#131—534no—
493C2×#131—534no—
494C22×M16—531no—
495C22×M16—534no—
496C22×M16C2×D5311yescharacteristic, complemented
497#520—534no—
498#520—534no—
499#520—1062no—
500#520—1062no—
501C2×C4×Q8—1061no—
502C2×C4×D4—1061no—
503C2×C4×D4—1062no—
504C2×#117—532no—
505C2×#117C2×D5311yescharacteristic, complemented
506C22×C4⋊C4—531no—
507C22×C4⋊C4—532no—
508#419—532no—
509#419—538no—
510#419C2×D5312yescomplemented
511#418—532no—
512#418—538no—
513#418C2×D5312yescomplemented
514#417—534no—
515#417—534no—
516#417—534no—
517#417—534no—
518#417—532no—
519#417—532no—
520#417—538no—
521#417—538no—
522#417C2×D5312yescomplemented
523#417C2×D5312yescomplemented
524#416—534no—
525#416—538no—
526#416—538no—
527#416C2×D5314yescomplemented
528C2×#103—532no—
529C2×#103—532no—
530C2×#103—538no—
531C2×#102—532no—
532C2×#102—532no—
533C2×#102—538no—
534C53#6008911yescharacteristic, complemented, Sylow
5352−1+4—5316no—
5362−1+4—5316no—
5372−1+4—1068no—
5382−1+4—10616no—
5392−1+4—1068no—
540H(5,𝔽2)—5316no—
541H(5,𝔽2)—5316no—
542H(5,𝔽2)—10632no—
543H(5,𝔽2)—1068no—
544H(5,𝔽2)—10616no—
545H(5,𝔽2)—1068no—
546C2×#41—21no—
547C2×#41—21no—
548C2×#41—24no—
549C2×#41—538no—
550C2×#41—532no—
551C2×#41—532no—
552C2×#41—538no—
553C2×#41—532no—
554C2×#41—532no—
555C2×#41—5332no—
556C2×#41—534no—
557C2×#41—534no—
558C2×#41—538no—
559C2×#41—532no—
560C2×#41—532no—
561C2×#41—1064no—
562C2×#41—1064no—
563C2×#41—1062no—
564C2×#41—1062no—
565C2×#41—10632no—
566C2×#41—1064no—
567C2×#41—10616no—
568C2×#41—1064no—
569C2×#41—1062no—
570C2×#41—1062no—
571C2×#41—10632no—
572C2×#41—1061no—
573C2×#41—1061no—
574C2×#41—1064no—
575C2×#41C4×D5318yescomplemented
576C2×#41C22×D5312yes—
577C2×#41C22×D5312yes—
578C22×Q8—531no—
579C22×Q8—534no—
580C22×Q8—531no—
581C22×Q8—1062no—
582C22×Q8—1062no—
583C22×Q8C22×D5311yescharacteristic
584C22×D4—21no—
585C22×D4—532no—
586C22×D4—534no—
587C22×D4—531no—
588C22×D4—531no—
589C22×D4—1062no—
590C22×D4—1064no—
591C22×D4—1062no—
592C22×D4—1064no—
593C22×D4—1064no—
594C22×D4—1061no—
595C22×D4C22×D5311yescharacteristic
596C23×C4—21no—
597C23×C4—532no—
598C23×C4—1064no—
599C23×C4—1062no—
600C23×C4—1061no—
601C23×C4—1061no—
602C23×C4C22×D5311yescharacteristic
603#131—10616no—
604#131—10616no—
605C2×M16—24no—
606C2×M16—532no—
607C2×M16—532no—
608C2×M16—538no—
609C2×M16—10616no—
610C2×M16—1064no—
611C2×M16C22×D5312yes—
612C2×M16C22×D5312yes—
613C22×C8—532no—
614C22×C8—538no—
615C22×C8C22×D5312yes—
616C4×Q8—1064no—
617C4×Q8—1064no—
618C4×D4—1064no—
619C4×D4—1064no—
620C4×D4—1068no—
621C4×D4—1068no—
622#117—21no—
623#117—21no—
624#117—538no—
625#117—1064no—
626#117C22×D5312yes—
627#117C22×D5312yes—
628C2×C4⋊C4—532no—
629C2×C4⋊C4—532no—
630C2×C4⋊C4—532no—
631C2×C4⋊C4—538no—
632C2×C4⋊C4—1064no—
633C2×C4⋊C4—1062no—
634C2×C4⋊C4—1061no—
635C2×C4⋊C4—1061no—
636C2×C4⋊C4—1061no—
637C2×C4⋊C4C22×D5311yescharacteristic
638C2×C4⋊C4C22×D5311yescharacteristic
639C2×C22⋊C4—21no—
640C2×C22⋊C4—1062no—
641C2×C42—21no—
642C2×C42—1062no—
643#103—538no—
644#103—538no—
645#103—534no—
646#103—534no—
647#103C22×D5314yes—
648#103C22×D5314yes—
649#102—538no—
650#102—538no—
651#102—534no—
652#102—534no—
653#102C22×D5314yes—
654#102C22×D5314yes—
655C24—21no—
656C24—532no—
657C24—1064no—
658C24—1061no—
659C24D4×D5311yescharacteristic
660#41—28no—
661#41—28no—
662#41—24no—
663#41—24no—
664#41—5316no—
665#41—5316no—
666#41—538no—
667#41—538no—
668#41—538no—
669#41—538no—
670#41—5316no—
671#41—5316no—
672#41—538no—
673#41—538no—
674#41—10632no—
675#41—10632no—
676#41—10616no—
677#41—10616no—
678#41—10632no—
679#41—1068no—
680#41—1068no—
681#41—10632no—
682#41—10616no—
683#41—10616no—
684#41—1068no—
685#41—1068no—
686#41—1064no—
687#41—1064no—
688#41C2×C4×D5318yes—
689#41C2×C4×D5318yescomplemented
690C2×Q8—21no—
691C2×Q8—22no—
692C2×Q8—538no—
693C2×Q8—532no—
694C2×Q8—532no—
695C2×Q8—5316no—
696C2×Q8—534no—
697C2×Q8—532no—
698C2×Q8—1064no—
699C2×Q8—10616no—
700C2×Q8—1068no—
701C2×Q8—10616no—
702C2×Q8—1061no—
703C2×Q8—1062no—
704C2×Q8C2×C4×D5314yescomplemented
705C2×Q8C23×D5312yes—
706C2×D4—28no—
707C2×D4—22no—
708C2×D4—22no—
709C2×D4—21no—
710C2×D4—22no—
711C2×D4—5316no—
712C2×D4—534no—
713C2×D4—534no—
714C2×D4—5316no—
715C2×D4—538no—
716C2×D4—534no—
717C2×D4—532no—
718C2×D4—532no—
719C2×D4—532no—
720C2×D4—10616no—
721C2×D4—1064no—
722C2×D4—1068no—
723C2×D4—1064no—
724C2×D4—10632no—
725C2×D4—10616no—
726C2×D4—10632no—
727C2×D4—10632no—
728C2×D4—1064no—
729C2×D4—1068no—
730C2×D4—1062no—
731C2×D4—1062no—
732C2×D4—1061no—
733C2×D4—1062no—
734C2×D4C2×C4×D5314yescomplemented
735C2×D4C23×D5312yes—
736C22×C4—21no—
737C22×C4—28no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—532no—
743C22×C4—538no—
744C22×C4—534no—
745C22×C4—538no—
746C22×C4—534no—
747C22×C4—1064no—
748C22×C4—10632no—
749C22×C4—1064no—
750C22×C4—1068no—
751C22×C4—1064no—
752C22×C4—1061no—
753C22×C4—1068no—
754C22×C4—1062no—
755C22×C4—1062no—
756C22×C4—1062no—
757C22×C4—1062no—
758C22×C4—1062no—
759C22×C4—4244no—
760C22×C4—4242no—
761C22×C4C2×C4×D5314yes—
762C22×C4D4×D5311yescharacteristic
763C22×C4D4×D5311yescharacteristic
764C22×C4D4×D5311yescharacteristic
765C22×C4D4×D5314yes—
766C22×C4C23×D5311yescharacteristic
767C22×C4C23×D5311yescharacteristic
768C22×C4C23×D5311yescharacteristic
769M16—24no—
770M16—24no—
771M16—10616no—
772M16—1064no—
773M16—1064no—
774C2×C8—24no—
775C2×C8—534no—
776C2×C8—10616no—
777C2×C8—1064no—
778C2×C8C23×D5314yes—
779C4⋊C4—21no—
780C4⋊C4—21no—
781C4⋊C4—534no—
782C4⋊C4—1068no—
783C4⋊C4—1062no—
784C4⋊C4—1062no—
785C4⋊C4—1062no—
786C4⋊C4C23×D5312yes—
787C4⋊C4C23×D5312yes—
788C22⋊C4—22no—
789C22⋊C4—22no—
790C22⋊C4—1068no—
791C42—22no—
792C42—22no—
793C42—1068no—
794C23—22no—
795C23—24no—
796C23—41no—
797C23—41no—
798C23—81no—
799C23—81no—
800C23—534no—
801C23—538no—
802C23—10616no—
803C23—1064no—
804C23—1062no—
805C23—4241no—
806C23—4241no—
807C23—4244no—
808C23—4244no—
809C23—2122no—
810C23—2122no—
811C23C22⋊C4×D5314yes—
812C23C2×D4×D5311yescharacteristic
813C23C2×D4×D5311yescharacteristic
814C23C2×D4×D5311yescharacteristic
815Q8—24no—
816Q8—22no—
817Q8—538no—
818Q8—538no—
819Q8—534no—
820Q8—10616no—
821Q8—1064no—
822Q8—1062no—
823Q8C22×C4×D5314yes—
824D4—28no—
825D4—28no—
826D4—24no—
827D4—22no—
828D4—5316no—
829D4—5316no—
830D4—538no—
831D4—538no—
832D4—534no—
833D4—10616no—
834D4—10616no—
835D4—10616no—
836D4—1068no—
837D4—1068no—
838D4—1064no—
839D4—1062no—
840D4C22×C4×D5314yes—
841C2×C4—24no—
842C2×C4—22no—
843C2×C4—28no—
844C2×C4—28no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—538no—
850C2×C4—534no—
851C2×C4—5316no—
852C2×C4—538no—
853C2×C4—538no—
854C2×C4—10616no—
855C2×C4—10616no—
856C2×C4—10616no—
857C2×C4—1064no—
858C2×C4—1062no—
859C2×C4—1068no—
860C2×C4—1068no—
861C2×C4—1064no—
862C2×C4—4248no—
863C2×C4—4242no—
864C2×C4—4242no—
865C2×C4—2124no—
866C2×C4C22⋊C4×D5314yes—
867C2×C4C22⋊C4×D5314yes—
868C2×C4C22⋊C4×D5314yes—
869C2×C4C22×C4×D5312yes—
870C2×C4C22×C4×D5312yes—
871C2×C4C22×C4×D5312yes—
872C2×C4C2×D4×D5311yescharacteristic
873C2×C4C2×D4×D5311yescharacteristic
874C2×C4C2×D4×D5311yescharacteristic
875C2×C4C2×D4×D5312yes—
876C2×C4C2×D4×D5312yes—
877C2×C4C2×D4×D5312yes—
878C2×C4C24×D5311yescharacteristic
879C8—24no—
880C8—1064no—
881C22—21no—
882C22—21no—
883C22—21no—
884C22—21no—
885C22—21no—
886C22—21no—
887C22—24no—
888C22—44no—
889C22—42no—
890C22—42no—
891C22—84no—
892C22—538no—
893C22—1064no—
894C22—1064no—
895C22—1064no—
896C22—4244no—
897C22—42416no—
898C22—2128no—
899C22—2122no—
900C22—2122no—
901C22C2×C22⋊C4×D5312yes—
902C22C2×C22⋊C4×D5312yes—
903C22C2×C22⋊C4×D5312yes—
904C22C22×D4×D5311yescharacteristic
905C4—24no—
906C4—42no—
907C4—42no—
908C4—538no—
909C4—1064no—
910C4—2124no—
911C4C2×C22⋊C4×D5312yes—
912C4C2×C22⋊C4×D5312yes—
913C4C2×C22⋊C4×D5312yes—
914C4C23×C4×D5311yescharacteristic
915C4C22×D4×D5311yescharacteristic
916C2—22no—
917C2—22no—
918C2—22no—
919C2—44no—
920C2—1068no—
921C2—2124no—
922C2C22×C22⋊C4×D5311yescharacteristic
923C2#2028949211yescharacteristic
924C2#2028949911yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutatorC4×C53C24×C4
FrattiniC2×C4C24×D53
FittingC53×#2896C2
socleC22×C53C23×D4
prime radicalC2×#16811459C2
cosocleC2×C4×C53C25
hypercenter#2896D53
hypocenterC53#60089
LCSG ▷ C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2896

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#16811389C2semidirect
3. C2×#16811103C2semidirect
4. #20283247C2semidirect
5. #20283244C2semidirect
6. #20283240C2semidirect
7. #20283237C2semidirect
8. #20283232C2semidirect
9. #20283231C2semidirect
10. C2×#16810625C2semidirect
11. C2×#16810624C2semidirect
12. #417×D53C2semidirect
13. C53×#2896C2semidirect
15. #16811459C4semidirect
29. C2×#13133225C22semidirect
30. C2×#13133223C22semidirect
31. C22×#11719917C22semidirect
32. C2×M16×D53C22semidirect
35. #16811103C22semidirect
36. #16811103C22semidirect
40. C2×#13133175C22semidirect
41. C22×C4⋊Dic53C22semidirect
42. C2×C4⋊C4×D53C22semidirect
43. #16810631C22semidirect
44. #16810630C22semidirect
45. #16810627C22semidirect
46. #16810626C22semidirect
47. #16810625C22semidirect
48. #16810625C22semidirect
49. #16810624C22semidirect
50. #16810624C22semidirect
51. #16810623C22semidirect
52. #16810622C22semidirect
53. #16810622C22semidirect
54. #16810621C22semidirect
55. #16810618C22semidirect
56. #16810617C22semidirect
57. #16810616C22semidirect
58. C2×#13133142C22semidirect
59. C2×#13133141C22semidirect
60. #103×D53C22semidirect
61. C2×#13133139C22semidirect
62. C2×#13133138C22semidirect
63. #102×D53C22semidirect
65. C22×M16×C53C22semidirect
66. C2×#117×C53C22semidirect
67. C53×#419C22semidirect
68. C53×#418C22semidirect
69. C53×#417C22semidirect
70. C53×#417C22semidirect
71. C53×#416C22semidirect
73. #13133265C2×C4semidirect
76. #13133264C2×C4semidirect
79. #13133263C2×C4semidirect
82. #13133262C2×C4semidirect
94. C2×#11719945C2×C4semidirect
108. #41×D53C2×C4semidirect
168. C2×#41×C53C2×C4semidirect
202. #41×C53C22×C4semidirect
205. C2×Q8×C53C22×C4semidirect
212. C2×D4×C53C22×C4semidirect
246. #11719949C22×C4semidirect
249. Q8×D53C22×C4semidirect
254. #11719947C22×C4semidirect
259. D4×D53C22×C4semidirect
273. #11719945C22×C4semidirect
281. C2×D212C22×C4semidirect
302. C2×Dic106C22×C4semidirect
463. #2896D53semidirect
496. C22×M16C2×D53semidirect
505. C2×#117C2×D53semidirect
510. #419C2×D53semidirect
513. #418C2×D53semidirect
522. #417C2×D53semidirect
523. #417C2×D53semidirect
527. #416C2×D53semidirect
534. C53#60089semidirect
575. C2×#41C4×D53semidirect
689. #41C2×C4×D53semidirect
704. C2×Q8C2×C4×D53semidirect
734. C2×D4C2×C4×D53semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168114592
C2×#168113892
C2×#168111032
#202832472
#202832442
#202832402
#202832372
#202832322
#202832312
C2×#168106252
C2×#168106242
#417×D532
C53×#28962
#6008953